|Lot of build up here, nice narrative, and the only problems I found can easily be spotted by a beta reader or a very mean, heartless second draft from yourself lol. (I have a problem with redrafting my own stuff, because I know how it's supposed to sound in my head, so I just gloss over my errors.)
Firstly, there are several things that come to attention but these are nit-picking things, and please don't take them personal if my suggestions offend your style; this is just how I see thing.
'And they would be back on solid ground in less than three days anyway.' "And" doesn't start this sentence well. By old grammatical standards, it's improper, and while I often ignore these rules, the "And" just doesn't work here.
'And Arreton lake.' The "And" works here, but the lake should be capitalized: Arreton Lake
'The small area had withstood time and despite the fact that it was quiet and almost deserted at the best of times, it was one of the few places she could keep to herself.' This sentence is a bit confusing. '..despite the face it was...almost deserted, it was one of the few places she could keep to herself.' It's easier to keep to yourself when no one's around. I'd rethink the contrast/comparison here.
'... push Rhodes’ words of chiding out of my head.' Should have said HER head.
Like I said, a revision of this with a fresh set of eyes (hopefully still in their owners head) would catch these kinds of things. I think it is a good start, but the place where you left off (her going into the gym to run laps) didn't leave me with a sense of conflict to make me want to delve into the next chapter. The engineer in the kitchen and the mention of his odd humming and talking to the engine, now that was cool. Best of luck on this, I hope my review was helpful in some way. Take it easy.